Asymptotic behavior of the generalized Derrida-Retaux recursive model
Probability
2025-08-19 v3
Abstract
We study the max-type recursive model introduced by Hu and Shi (J. Stat. Phys., 2018), which generalizes the model of Derrida and Retaux (J. Stat. Phys., 2014). The class of geometric-type marginal distributions is preserved by the model with a geometric offspring distribution. We give some long-time asymptotic expansions of the parameters of the marginal distribution. From the expansions, we derive the asymptotics of the sustainability probability, marginal distribution, first moment and probability generating function.
Keywords
Cite
@article{arxiv.2411.13068,
title = {Asymptotic behavior of the generalized Derrida-Retaux recursive model},
author = {Zenghu Li and Run Zhang},
journal= {arXiv preprint arXiv:2411.13068},
year = {2025}
}
Comments
19 pages, Version: 2025-08-18